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What is the simplified form of 3a^4b^-2c^3?
a. (81a^4c^3)/(b^2)
b. (81a^4)/(b^2c^3)
c. (3a^4)/(b^2c^3)
d. (3a^4c^3)/(b^2) D What is -a^-2 if a = -5?
a. -25
b. 25
c. -1/25
d. 1/25 D What is (-m)^-3n if m = 2 and n = -24?
a. 3
b. -3
c. 4
d. -4 A

Respuesta :

HomertheGenius
1. Simplified form of:   3 a^4 * 4 b^(-2) * c^3 =
= ( 3 a^4 * 4 c^3 ) / ( b^2 )
Answer: d.
2.  If a = - 5,
- a^(-2) = - ( - 5 )^(-2) = - ( 1/ 5^2 ) = - 1/25
Answer: c.
3. If m = 2 and n = - 24:
( - 2 )^(-3) * ( - 24 ) = 1 / (- 2 )^3  * ( - 24 ) = - 1 / 8 * ( - 24 ) = 24 / 8 = 3
Answer: a. 3

Answer:

1. The correct option is d.

2. The correct option is c.

3. The correct option is a.

Step-by-step explanation:

1.

The given expression is

[tex]3a^4b^{-2}c^3[/tex]

Using property of exponent the given expression can be written as

[tex]\frac{3a^4c^3}{b^{2}}[/tex]               [tex][\because a^{-n}=\frac{1}{a^n}][/tex]

Therefore, the correct option is d.

2.

The given expression is

[tex]-a^{-2}[/tex]

Using property of exponent the given expression can be written as

[tex]-\frac{1}{a^{2}}[/tex]               [tex][\because a^{-n}=\frac{1}{a^n}][/tex]

Put a=-5

[tex]-\frac{1}{(-5)^{2}}[/tex]

[tex]-\frac{1}{25}[/tex]

Therefore option c is correct.

3.

The given expression is

[tex](-m)^{-3}n[/tex]

Using property of exponent the given expression can be written as

[tex]\frac{n}{(-m)^3}[/tex]

Put m=2 and n=-24.

[tex]\frac{-24}{(-2)^3}[/tex]

[tex]\frac{-24}{-8}[/tex]

[tex]\frac{24}{8}=3[/tex]

Therefore option a is correct.

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